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Just a year before his death in 1920 at the age of 32, mathematician Srinivasa Ramanujan came upon a remarkable pattern in a special list of whole numbers.

The list represented counts of how many ways a given whole number can be expressed as a sum of positive integers. For example, 4 can be written as 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. Including 4 itself but...